The Bi-directional Reflectance Distribution Function (BRDF) of a surface area element assigns transfer coefficients to each pair of incident angles and reflected/scattered angles. These coefficients translate from incoming irradiance/illuminance to outgoing radiance/luminance and take the form of a ratio. When sampling a point like region over extended solid angles, the obtained BRDF is a function of 4 scalars denoting angles and characterizes a fundamental optical property of the surface at this location. The result is dependent on polarization, wavelength, coherence, etc. of the probing light and may differ for different positions on a surface. It can be appreciated that the high dimensional signature conveyed by a BRDF may serve as proxy for material properties, the relevance of which extends well beyond the field of optics. Many fields employ BRDF measurements, or subsets of it, for applications including medical diagnostics, anti-counterfeiting, gloss evaluation, printing media recognition, optical design and computer graphics.
Materials can have unique values of these properties and one may build a library of known materials and their properties. When an unknown sample is encountered, the BRDF measurement results may indicate the type of material. Known materials may also undergo measurement to determine the properties of the surface and from those properties may convey information about architecture, general product design, paint development, topography, materials fabrication, print quality, coatings and other situation when the appearance of a surface is important.
Typically, the BRDF measurement requires the measurement of the scattered light intensity from a surface and its dependence upon the incident and scattered angles, for any particular illumination wavelength. These measurements are typically done using a collimated light source and an individual detector that is moved to different scattering angles for each angle of incidence. For each angle of incidence, the number of positions of the detector, the signal integration time, the time to move the detector and the number of wavelengths combine to make the measurement rather slow. In addition, the apparatus used to make such a measurement is rather large, in part because the mechanics needed to move the detector from position to position. A more compact BRDF system is needed, as well as one that is faster and less expensive.